# The specific heat of steel is 420 J/(kg°C). How much energy is required to heat 1 kg of steel by 20 °C?

Jan 7, 2017

$\text{8400 J}$

#### Explanation:

The specific heat of a substance tells you how much heat is required in order to heat one unit of mass, usually $\text{1 g}$, of that substance by ${1}^{\circ} \text{C}$.

In this case, the specific heat of steel uses $\text{1 kg}$ as the unit of mass, which means that the value given to you tells you how much heat is required in order to heat $\text{1 kg}$ of steel by ${1}^{\circ} \text{C}$.

Since you have

$c = {\text{420 J kg"^(-1)""^@"C}}^{- 1}$

you can say that you need $\text{420 J}$ of heat in order to increase the temperature of $\text{1 kg}$ of steel by ${1}^{\circ} \text{C}$.

This means that in order to increase the temperature of a given mass of steel by ${20}^{\circ} \text{C}$, you'd need

20 color(red)(cancel(color(black)(""^@"C"))) * "420 J"/("1 kg" color(red)(cancel(color(black)(""^@"C")))) = "8400 J kg"^(-1)

For $\text{1 kg}$, this gives you

$1 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{kg"))) * "8400 J"/(1color(red)(cancel(color(black)("kg")))) = color(darkgreen)(ul(color(black)("8400 J}}}}$

I'll leave the answer rounded to two sig figs.